563 research outputs found
Intelligent escalation and the principle of relativity
Escalation is the fact that in a game (for instance in an auction), the
agents play forever. The -game is an extremely simple infinite game with
intelligent agents in which escalation arises. It shows at the light of
research on cognitive psychology the difference between intelligence
(algorithmic mind) and rationality (algorithmic and reflective mind) in
decision processes. It also shows that depending on the point of view (inside
or outside) the rationality of the agent may change which is proposed to be
called the principle of relativity.Comment: arXiv admin note: substantial text overlap with arXiv:1306.228
Boltzmann samplers for random generation of lambda terms
Randomly generating structured objects is important in testing and optimizing
functional programs, whereas generating random -terms is more specifically
needed for testing and optimizing compilers. For that a tool called QuickCheck
has been proposed, but in this tool the control of the random generation is
left to the programmer. Ten years ago, a method called Boltzmann samplers has
been proposed to generate combinatorial structures. In this paper, we show how
Boltzmann samplers can be developed to generate lambda-terms, but also other
data structures like trees. These samplers rely on a critical value which
parameters the main random selector and which is exhibited here with
explanations on how it is computed. Haskell programs are proposed to show how
samplers are actually implemented
(Mechanical) Reasoning on Infinite Extensive Games
In order to better understand reasoning involved in analyzing infinite games
in extensive form, we performed experiments in the proof assistant Coq that are
reported here.Comment: 11
The risk of divergence
We present infinite extensive strategy profiles with perfect information and
we show that replacing finite by infinite changes the notions and the reasoning
tools. The presentation uses a formalism recently developed by logicians and
computer science theoreticians, called coinduction. This builds a bridge
between economic game theory and the most recent advance in theoretical
computer science and logic. The key result is that rational agents may have
strategy leading to divergence .Comment: 3rd International Workshop on Strategic Reasoning, Dec 2015, Oxford,
United Kingdom. 201
On the enumeration of closures and environments with an application to random generation
Environments and closures are two of the main ingredients of evaluation in
lambda-calculus. A closure is a pair consisting of a lambda-term and an
environment, whereas an environment is a list of lambda-terms assigned to free
variables. In this paper we investigate some dynamic aspects of evaluation in
lambda-calculus considering the quantitative, combinatorial properties of
environments and closures. Focusing on two classes of environments and
closures, namely the so-called plain and closed ones, we consider the problem
of their asymptotic counting and effective random generation. We provide an
asymptotic approximation of the number of both plain environments and closures
of size . Using the associated generating functions, we construct effective
samplers for both classes of combinatorial structures. Finally, we discuss the
related problem of asymptotic counting and random generation of closed
environemnts and closures
Counting and Generating Terms in the Binary Lambda Calculus (Extended version)
In a paper entitled Binary lambda calculus and combinatory logic, John Tromp
presents a simple way of encoding lambda calculus terms as binary sequences. In
what follows, we study the numbers of binary strings of a given size that
represent lambda terms and derive results from their generating functions,
especially that the number of terms of size n grows roughly like 1.963447954.
.. n. In a second part we use this approach to generate random lambda terms
using Boltzmann samplers.Comment: extended version of arXiv:1401.037
On the Rationality of Escalation
Escalation is a typical feature of infinite games. Therefore tools conceived
for studying infinite mathematical structures, namely those deriving from
coinduction are essential. Here we use coinduction, or backward coinduction (to
show its connection with the same concept for finite games) to study carefully
and formally the infinite games especially those called dollar auctions, which
are considered as the paradigm of escalation. Unlike what is commonly admitted,
we show that, provided one assumes that the other agent will always stop,
bidding is rational, because it results in a subgame perfect equilibrium. We
show that this is not the only rational strategy profile (the only subgame
perfect equilibrium). Indeed if an agent stops and will stop at every step, we
claim that he is rational as well, if one admits that his opponent will never
stop, because this corresponds to a subgame perfect equilibrium. Amazingly, in
the infinite dollar auction game, the behavior in which both agents stop at
each step is not a Nash equilibrium, hence is not a subgame perfect
equilibrium, hence is not rational.Comment: 19 p. This paper is a duplicate of arXiv:1004.525
Dynamic Logic of Common Knowledge in a Proof Assistant
Common Knowledge Logic is meant to describe situations of the real world
where a group of agents is involved. These agents share knowledge and make
strong statements on the knowledge of the other agents (the so called
\emph{common knowledge}). But as we know, the real world changes and overall
information on what is known about the world changes as well. The changes are
described by dynamic logic. To describe knowledge changes, dynamic logic should
be combined with logic of common knowledge. In this paper we describe
experiments which we have made about the integration in a unique framework of
common knowledge logic and dynamic logic in the proof assistant \Coq. This
results in a set of fully checked proofs for readable statements. We describe
the framework and how a proof can beComment: 15
HedN Game, a Relational Framework for Network Based Cooperation
This paper proposes a new framework for cooperative games based on mathematical relations. Here cooperation is defined as a supportive partnerships represented by a directed network between players (aka hedonic relation). We examine in a specific context, modeled by abstract games how a change of supports induces a modification of strategic interactions between players. Two levels of description are considered: the first one describes the support network formation whereas the second one models the strategic interactions between players. Both are described in a unified formalism, namely CP~game. Stability conditions are stated, emphasizing the connection between these two levels. We also stress the interaction between updates of supports and their impact on the evolution of the context.Cooperative Game, Network, Stability, Hedonic Relation
Les crashs sont rationnels
As we show by using notions of equilibrium in infinite sequential games,
crashes or financial escalations are rational for economic or environmental
agents, who have a vision of an infinite world. This contradicts a picture of a
self-regulating, wise and pacific economic world. In other words, in this
context, equilibrium is not synonymous of stability. We try to draw, from this
statement, methodological consequences and new ways of thinking, especially in
economic game theory. Among those new paths, coinduction is the basis of our
reasoning in infinite games
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